| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Geometry of Submanifolds II | MAT549 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Res. Assist. Zehra İŞBİLİR |
| Instructors | |
| Assistants | |
| Goals | To examine submanifolds and teach basic equations. |
| Course Content | Compact manifold, orientable manifold, Riemannian manifold, Christoffel symbols, covariant derivative on a submanifold, Riemannian connection, Riemann-Christoffel curvature tensor, sectional curvature, Complete Riemannian manifold, isometric manifolds, conformal manifolds, Space form, Reduced connection on submanifolds, second fundamental form, Normal bundle, normal connection, total geodesic submanifold, pseudo ombilical submanifold. |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics - Students will learn how to read academical journals |
| Week | Topics | Learning Methods |
|---|---|---|
| 0. Week | Space form | |
| 1. Week | Compakt and directionable manifolds | |
| 2. Week | Christoffel symbols, covariant derivative | |
| 3. Week | Riemann-Christoffel curvature tensor | |
| 4. Week | Sectional curvature | Course Hours Preparation, After Class Study Research Other Activities |
| 5. Week | Complete Riemannian manifold | |
| 6. Week | Conformal manifolds | |
| 7. Week | Isometric manifolds | |
| 8. Week | Midterm | |
| 9. Week | Reduced connection in submanifolds | |
| 10. Week | Second Fundamental Form | |
| 11. Week | Normal bunch | |
| 12. Week | Normal connection | |
| 13. Week | Total geodesic submanifold | |
| 14. Week | Pseudo omnibus submanifold |
| Bang-yen Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973. Aminov, Yu. A. The Geometry of Submanifolds. Gordon and Breach Science Publishers, Singapore, 2001. |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 2 | 0 | 0 | 40,60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 2 | 28 |
| Final | 1 | 12 | 12 |
| Practice | 14 | 3 | 42 |
| Practice End-Of-Term | 15 | 3 | 45 |
| Classroom Activities | 14 | 3 | 42 |
| Total Workload | 199 | ||
| ECTS Credit of the Course | 8.0 | ||
